That is common in Russia and Ukraine, too. You break a glass and shout the local counterpart to mazel tov (Russian/Ukrainian: "na shchast(ye/ia)"). Weddings are exclusive in that it's done intentionally. When you break something by accident at any other time you also whisper "for good luck".

I'm replying in my capacity as a curious Jew (don't let my ultra-faux-Nordic screen name fool you!) - but this is one of those "disputed customs" for which nobody really has a cite-able reason (as in "here in the Talmud/Zohar/Torah we are instructed to x because y" as is the case with a lot of Jewish custom). That being said, a lot of people have their opinions and rationale. Here are the ones I've heard of (citations and regional origin where available).

I asked my Bubbie at a wedding when I was small basically every question about everything, the explanation given to me by her (Ashkenazim from Hungary emigrated to Serbia emigrated to US) was that the breaking of a whole glass into pieces symbolized that the marriage was now 'permanent' in that it would be as impossible to break the marriage as it would be to put the glass back together. Never got the chance to ask her where she'd hear this (Rabbi?), but our family kept some traditions other Jewish families of different pedigree did not so maybe it's a regional explanation (we, for instance, always had an all dairy meal on a night of Chanukah to honor Yehudit [aka Judith of Judith and Holofernes] which not a lot of the primarily German-Jews in our area seem to hold to). But in this case - a hearty "Mazel Tov!" would appear to be called for because who likes divorce?

Being Ashkenazim, I did not know what the Sephardic view on the custom was, but during some ceremonies the groom says "If I forget thee Jerusalem let my right hand wither" before stomping the glass and symbolizing the destruction of Israel and the Temple and the general scattering of the Jewish people. In which case it would not be a good time to "Mazel Tov!" as you'd essentially be cheering the destruction of the Temple. (here is an article detailing criticisms given by former Sephardic chief Rabbi in Israel Rabbi Ovadia Yosef about cheering during the glass breaking - http://www.israelnationalnews.com/News/News.aspx/135988#.U3_dHC82zzM)

And last but not least, surly Jewish humor maintains that the groom stomps the glass at the wedding because it's his last chance to put his foot down. Har har.